Mr. Lee:

If you are using a square wave that is not centered around 0, for example if
it goes from 0 to 10 volts, then it approximates a sine wave
V = Vac sin(w * t) + Vdc
where Vac = Vdc = 5 volts, and w is the frequency.  Since the force on the
combdrive goes as the square of the voltage, the force is proportional to

V^2 = [Vac * sin(w t)]^2 + Vac * Vdc * sin(w * t) + Vdc ^2
    = Vac^2 * sin(2 * w * t) + Vac * Vdc * sin(w t) + Vdc ^2

so there are two dominant frequency terms -- one at the frequency w, and one
at 2 w.  You are driving with a square wave, so things are even messier
since there is energy in a large range of different frequencies.

I would recommend driving with a sine wave instead of a square wave.  If
you're having trouble finding a high-voltage sine wave generator, try using
a transformer to convert a low voltage sine wave into a high voltage sine
wave (it's really easy, and MUCH cheaper than buying equipment to generate a
high voltage sine wave).

Good luck!

***********************************
Robert Conant
BSAC / UC Berkeley
Berkeley CA, 94720-1774
rconant@bsac.eecs.berkeley.edu
http://www-bsac.eecs.berkeley.edu
***********************************


-----Original Message-----
From: Chua Bee Lee [mailto:eng50250@leonis.nus.edu.sg]
Sent: Thursday, February 11, 1999 5:35 AM
To: MEMS@ISI.EDU
Subject: Multiple Resonance Frequencies


Dear All,
        I have been working on folded beams resonators using square waves
to drive them. As I adjusted the driving frequency towards the resonance
value, I observed resonance at smaller amplitudes  at lower frequencies
prior to the one that I was expecting. I would appreciate if someone can
provide some insight on that.

        Thank you.
        CHUA Bee Lee
        Department of Mechanical and Production Engineering
        National University of Singapore